Question

attempt not accepted -- please submit answers again (or request new version if neccessary).
consider the graph of the function ( f(x) ):
evaluate the following integrals by interpreting them in terms of areas:
(a) ( int_{0}^{2} f(x) d x= )
(b) ( int_{0}^{2} f(x) d x= )
(c) ( int_{5}^{7} f(x) d x= )
(d) ( int_{0}^{7} f(x) d x= )

Explanation:

Step1: Use integral property

We know that \(\int_{0}^{7}f(x)dx=\int_{0}^{5}f(x)dx+\int_{5}^{7}f(x)dx\)

Step2: Substitute known values

Given \(\int_{0}^{5}f(x)dx = 10\) and \(\int_{5}^{7}f(x)dx=- 3\)

Step3: Calculate the result

\(\int_{0}^{7}f(x)dx=10+(-3)=7\)

Answer:

\(7\)